Equilibrium complex formation

STRATEGY First, we write the chemical equation for the equilibrium between the solid solute and the complex in solution as the sum of the equations for the solubility and complex formation equilibria. The equilibrium constant for the overall equilibrium is therefore the product of the equilibrium constants for the two processes. Then, we set up an equilibrium table and solve for the equilibrium concentrations of ions in solution. 

Equation (3) has good quantitative predictive power and is a successful extra-thermodynamic relationship like the Hammett sigma function. No other approach to modeling complex formation equilibria, including HSAB itself, can predict log values for unidentate ligands so accurately. 

The well-known tetrahedral [Co(NCS)4]2 ion has continued to attract attention from analytical chemists, physical chemists, and spectroscopists. The inelastic electron tunneling (IET) spectrum of (Me4N)2[Co(NCS)4] was compared with IR and Raman spectra of the same complex.359 The vibrational bands due to the Me4N+ were prominent in all three spectra, but Coligand stretches were absent from the IET spectra. The lowest 4 42 4T2 electronic transition was strong in the IET spectrum but absent from the IR spectrum. The electric dipole allowed 4A2 4TX electronic transition was observed in both the IET and IR spectra and no fine structure was observed. Complex formation equilibria between Co11 and SCN- were studied calorimetri-... 

Classical methods for the investigation of complex formation equilibria in solution (UV/Vis spectrometry, thermochemical and electrochemical techniques) are still in use (for an appraisal of these and other methods see, e.g., ref. 22). Examples for the determination of the ratio of metal to ligand in an Hg-protein complex by UV spectrometry are given in ref. 23, for the study of distributions of complex species of Cd in equilibria by combined UV spectrometry and potentio-metry in ref. 24 and by potentiometry alone in ref. 25, and for the combination of calorimetry and potentiometry to obtain thermodynamic data in ref. 26. 

The kinetic models for these reactions postulate fast complex-formation equilibria between the HA- form of ascorbic acid and the catalysts. The noted difference in the rate laws was rationalized by considering that some of the coordination sites remain unoccupied in the [Ru(HA)C12] complex. Thus, 02 can form a p-peroxo bridge between two monomer complexes [C12(HA)Ru-0-0-Ru(HA)C12]. The rate determining step is probably the decomposition of this species in an overall four-electron transfer process into A and H202. Again, this model does not postulate any change in the formal oxidation state of the catalyst during the reaction. 

The model proposed by Brandt et al. is consistent with the experimental observations, reproduces the peculiar shape of the kinetic curves in the absence and presence of dioxygen reasonably well, and predicts the same trends in the concentration dependencies of t, p that were observed experimentally (80). It was concluded that there is no need to assume the participation of oxo-complexes in the mechanism as it has been proposed in the literature (88-90). However, the model provides only a semi-quantitative description of the reaction because it was developed at constant pH by neglecting the acid-base equilibria of the sulfite ion and the reactive intermediates, as well as the possible complex-formation equilibria between various iron(III) species. In spite of the obvious constraints introduced by the simplifications, the results shed light on the general mechanistic features of the reaction and could be used to identify the main tasks for further model development. 

Some emphasis is given in the first two chapters to show that complex formation equilibria permit to predict quantitatively the extent of adsorption of H+, OH , of metal ions and ligands as a function of pH, solution variables and of surface characteristics. Although the surface chemistry of hydrous oxides is somewhat similar to that of reversible electrodes the charge development and sorption mechanism for oxides and other mineral surfaces are different. Charge development on hydrous oxides often results from coordinative interactions at the oxide surface. The surface coordinative model describes quantitatively how surface charge develops, and permits to incorporate the central features of the Electric Double Layer theory, above all the Gouy-Chapman diffuse double layer model. 

The central ion of a mineral surface (in this case we take for example the surface of a Fe(lll) oxide and S-OH corresponds to =Fe-OH) acts as Lewis acid and exchanges its stuctural OH against other ligands (ligand exchange). Table 2.1 lists the most important adsorption (= surface complex formation) equilibria. The following criteria are characteristic for all surface complexation models (Dzombak and Morel, 1990.)... 

Table 2.1 Adsorption (Surface Complex Formation Equilibria)...

We return to the complex formation equilibria described in Chapter 2 (Eqs. 2.1 -2.10). The equilibrium constants as given in these equations are essentially intrinsic constants valid for a (hypothetically) uncharged surface. In many cases we can use these constants as apparent constants (in a similar way as non-activity corrected constants are being used) to illustrate some of the principal features of the interdependent variables that affect adsorption. Although it is impossible to separate the chemical and electrical contribution to the total energy of interaction with a surface without making non-thermodynamic assumptions, it is useful to operationally break down the interaction energy into a chemical and a Coulombic part ... 

The Langmuir equation is derived here from application of the mass law, in a similar way as the surface complex formation equilibria were derived in Chapter 2. In principle at a constant pH there is no difference between a Langmuir constant and a surface complex formation constant. 

Surface protonation and deprotonation are experimentally directly accessible from alkalimetric or acidimetric surface tritrations. The surface concentrations (sMOH ) or <=MO") are nonlinearly related to H+ by surface complex formation equilibria or by semi-empirical relations in other words,... 

Szoekoe et al. (23) assume several parallel complex formation equilibria with different aggregates [the number of degrees of association is dependent on the bile salts (BS) concentration]. Each micelle with an iden-... 

Complex formation equilibria in binary mixtures of chloroform with dipropyl ether (PE), diisopropyl ether (IPE), methyl tert-butyl ether(MBE), tetrahydrofuran (THE), 1,4-dioxane (DOX), acetone (AC), and methyl acetate (MA) have been analyzed in detail. The complex formation equilibria in chloroform mixtures was compared to those previously examined for halothane (2-bromo-2-chloro-l,l,l-trifluoroethane) mixed with the same oxygenated solvents. It was found that the H-bonds formed by halothane are stronger than those formed by chloroform (Dohnal and Costas, 1996). 

Gl) have been measured at 293.15 K. Complex-formation equilibria for these four halothane-oxygenated solvent mixtures have been analyzed in detail using several association models (Dohnal et al., 1996). 

The kinetics (10) and the complex formation equilibria in the presence of nonionic micelles have been also investigated, at constant acidity. The stoichiometry was assessed by using Job s method and the apparent stability constants were evaluated according to Frank and Ostwald procedure (11), as previously reported for the systems iron/ sulfosalicylate and iron/salicylate in homogeneous aqueous acidic solution (12, 13). 

Hydrolysis and, more generally, complex formation equilibria may be described by cumulative stability constants, Using the Equations (3.28)-(3.31)... 

Ingri N. and Sillen L. G. (1962) High-speed computers as a supplement to graphical methods II. Some computer programs for studies of complex formation equilibria. Acta Chem. Scand. 16, I73-I9I. 

Of course, the problems of hydrolysis can be obviated by using non-aqueous solvents, and pseudo-metal ions have the necessary solubilities. For example, spectrophotometric studies (18) of complex formation equilibria between 2,2 -bipyridine (bipy) and dialkyltin dichloride have been reported. The log K values for complexes R2SnCl2-bipy are 3.19 (R, n-C4H9), 3.36 (R, CH3), and 6.7 (R, Cl) in acetonitrile. There is surprisingly little difference between the constants for dimethyl- and the dibutyltin dichloride complexes. The equilibrium constant for the dibutyl-tin dichloride complex increases with increasing dielectric constant of an alcohol solvent. 

Hydrolysis equilibria can be interpreted in a meaningful way if the solutions are not oversaturated with respect to the solid hydroxide or oxide. Occasionally, it is desirable to extend equilibrium calculations into the region of oversaturation but quantitative interpretations for the species distribution must not be made unless metastable supersaturation can be demonstrated to exist. Most hydrolysis equilibrium constants have been determined in the presence of a swamping inert electrolyte of constant ionic strength (/ = 0.1, 1, or 3 M). As we have seen before, the formation of hydroxo species can be formulated in terms of acid-base equilibria. The formulation of equilibria of hydrolysis reactions is in agreement with that generally used for complex formation equilibria (see Table 6.2). 

We will illustrate that surface complex formation equilibria permit us to predict quantitatively the extent of adsorption of H", OH of metal ions and ligands as a function of pH and solution variables and of surface characteristics. 

Table 9.1 presents the most important adsorption (= surface complex formation) equilibria. The following criteria are characteristic of all surface com-plexation models (Dzombak and Morel, 1990) ... 

Example 9.3. pH Dependence of Surface Complex Formation In order to exemplify simple complex formation equilibria, we calculate the pH depen-... 

If kj k n, then an equilibrium between the metal bound to the metal transport ligand and that in the water can be inferred (AT = kjkj) the uptake rate, determined by the free metal-ion concentration, is slow compared to the establishment of all other complex formation equilibria. 

Ligands such as ammonia, amines, and polyhydric alcohols may be exchanged between an external aqueous phase and resins carrying ions capable of forming coordination complexes, thus providing a powerful technique for studying complex ion structure and complex formation equilibria. 

List II summarizes schematically the type of surface complex formation equilibria that characterize the adsorption of H+, OH, cations, and ligands at a hydrous oxide surface. The various surface hydroxyls formed at a hydrous oxide surface may not be fully equivalent structurally and chemically. However, to facilitate the schematic representation of reactions and of equilibria, we will consider the chemical reaction of < a> surface hydroxyl group, S-OH. The following surface groups can be envisaged. 

Figure 7. The effect of ligands and metal ions on surface protonation of a hydrous oxide is illustrated by two examples (1). Part a Binding of a ligand (pH 7) to hematite, which increases surface protonation. Part h Adsorption of Pb2+ to hematite (pH 4.4), which reduces surface protonation. Part c Surface protonation of hematite alone as a function of pH (for comparison). All data were calculated with the following surface complex formation equilibria (1 = 5 X 10"3 M >. Electrostatic correction was made by diffuse double layer model.

H and 13C NMR spectra were used in a quantitative study of Al(II)-glutamate complex equilibria in solution.1095 27A1 NMR spectroscopy was able to identify species present in an equimolar Al(III)-citrate solution.1096 Complex formation equilibria were examined by 1H, 13C and 27A1 NMR spectra for the Al(III)-l-(+)-ascorbic acid system.1097 An NMR (1H, 13C) study has been nade of the Al(III) binding abilities of D-saccharinic and mucic acids.1098 27A1 NMR data were used to characterise fulvic acid-Al3+ complexes under acidic aqueous solutions.1099... 

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